Abstract
This paper derives an explicit solution of bilinear systems from the work of Wei and Norman about the solutions of homogeneous linear differential equations. This solution is based on the canonical basis of the Lie algebras spanned by the coefficient matrices, which are supposed to be solvable. The main achievement of this paper is an algorithm to compute these canonical basis.
The explicit solution then follows directly by a standard procedure from the results of Wei and Norman. The solution of bilinear systems is applied to the controllability of bilinear systems.
